Characteristics analysis of metal-clad and absorptive dielectric waveguides by a simple and accurate perturbation method

We present a simple and accurate method for characteristic analysis of metal-clad dielectric waveguides and absorptive waveguides. The real partN of the complex modal indexN=N + iN is obtained by solving the corresponding real eigenvalue equation, and the imaginary partN is given by (n/), where= + i is the complex dielectric constant of the absorptive layer, and N/ is obtained by numerical differentiation. The method is straightforward, and the cumbersome solution of complex transcendental equations is completely eliminated. Results for simple structures are in good agreement with those obtained by exact analysis.     

High resolution measurement of absorption μ(E) and anomalous dispersion f′(E) at theK-edge of copper

The variation with energyE of the X-ray absorption coefficient (E) and that of the anomalous dispersion correctionf(E) at the Cu-K-edge have been measured under identical experimental conditions using the X-ray interferometer installed in the Hamburger Synchrotronstrahlungslabor (HASYLAB) at the storage ring DORIS of DESY. The energy resolution achieved is E2 eV atE=9 keV. As a result of the extreme energy resolution in the near edge region up to about 60 eV above the edge, very detailed fine structures are observed in both (E) andf(E) which are tentatively attributed to multiple scattering resonances occuring in the scattering of the low energy photoelectron by neighbour atoms.The simultaneous measurement of (E) andf(E) opens the possibility to cross-correlate the experimental results with the help of Kramers-Kronig relations.     

The λϕ 3 4 field theory in a finite volume

The unnormalized doubly cutoff Schwinger functions converge as the ultraviolet cutoff is removed. The limits, the finite volume unnormalized Schwinger functions, are tempered distributions and areC in the coupling constant. They have asymptotic expansions given by perturbation theory. For sufficiently small they can be normalized and then they are the moments of a measure onI (IR³).Supported in part by the National Science Foundation under Grant GP 40354X.     

Über den Einfluss von Stickstopf auf die Exoelektronenemission von Germanium

Zusammenfassung Es wurde der Einfluß eines Bombardements mit Stickstoffionen vor der Erregung untersucht und gezeigt, daß die Stiekstoffatome eine große Rolle bei der Entstehung des Emissionsmaximums bei 150° spielen.

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, 150°C.

     

The modular group and super-KMS functionals

Every normal, faithful, self-adjoint functional on a von Neumann algebraA canonically determines a one-parameter-weakly continuous *-automorphism group (the analog of the modular group) and a canonical ₂ grading onA, commuting with . We show that the functional satisfies the weak super-KMS property with respect to and Furthermore, we prove that and are the unique pair of a-weakly continuous one-parameter *-automorphism group and a grading of the algebra, commuting with each other, with respect to which is weakly super-KMS. The above results thus provide a complete extension of the theory of Tomita and Takesaki to the nonpositive case.Supported in part by the National Science Foundation under Grant DMS-8922002.     

Correlations of Spin States for Icosahedral Double Group

The irreducible bases of the icosahedral double groups I and I_h are explicitly presented in their respective group spaces. Applying these bases to the spin states |j, , we obtain a simple formula for combining the spin states into the symmetry-adapted bases which belong to a given row of given irreducible representations of I and I_h.     

Small perturbations ofC*-dynamical systems

It is shown that if is the generator of a strongly continuous oneparameter group of *-automorphisms of aC*-algebraA and is an unbounded *-derivation ofA with the same domain as , then + is also a generator for all sufficiently small real numbers .     

A generalized representation for dielectric dispersion

The generalized formulation for dielectric dispersion is extended for dielectrics exhibiting strongly overlapping arcs in the- complex plane. Subsequently, a novel network representation is developed whereby Negative Impedance Converters (NICs) are employed along with passive R-C elements. Satisfactory agreement is obtained in comparing the experimental results with those calculated using the new formulation.     

The influence of successive asymmetrical magnetization reversal on the magnetic state of open samples

A study is made of the influence of successive asymmetrical magnetization reversal on the magnetic state of open samples, where the macroscopic demagnetization field has a significant effect during magnetization reversal and leads to a sort of rotation of the asymmetrical loops performed one after another. This effect is similar to reptation, which was studied experimentally by Nguyen van Dang [1–4] and theoretically explained by Néel [5, 6]. The quantitative expression of the rotation of asymmetrical loops in open samples as a function of the number of loops and amplitude of the disymmetry is similar to that with the reptation effect.

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In conclusion the authors thank Dr. L. Valenta, C. Sc., and Z. Málek, C. Sc., for valuable discussions.     

The van der Waals limit for classical systems

For a -dimensional system of particles with the two-body potentialq(r)+ ^v K(r) and density , it is proved under fairly weak conditions onq andK that the canonical pressure (, ) and chemical potential (, ) tend to definite limits when 0. The limiting functions are absolutely continuous and are given in terms of the derivative of the limiting free energy density which was found in Part I.     

Accurate calculation of functional determinants

A dependence of the functional determinant of the operator from the family D() satisfying the condition D()=fD()+D()f on the parameter m² of infrared regularization is found in the regularization method using a generalized function.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 6, pp. 27–32, June, 1988.     

Effect of quenching temperature on the components of the permeability tensor and the complex dielectric constant of microwave magnesium ferrites

We report an investigation of the effect of the quenching temperature (from 900 °C, 700 °C, and for self-cooling) on the components of the permeability tensor and on the complex dielectric constant * of magnesium-aluminum, magnesium-chromium and magnesium-manganese, ferrites of fixed composition. The measuring apparatus and measurement procedure are described and an estimate of the errors is given. It is shown that due to quenching the gyrotropic properties of the ferrites are increased ( falls and _a increases), while the dielectric constant is unchanged. Quenching leads to an increase in the magnetic and dielectric losses.Translated from Izvestiya VUZ. Fizika, Vol. 11, No. 11, pp. 41–47, November, 1968.     

Natural boundaries for area-preserving twist maps

We consider KAM invariant curves for generalizations of the standard map of the form (x, y)=(x+y, y+f(x)), wheref(x) is an odd trigonometric polynomial. We study numerically their analytic properties by a Padé approximant method applied to the function which conjugates the dynamics to a rotation +. In the complex plane, natural boundaries of different shapes are found. In the complex plane the analyticity region appears to be a strip bounded by a natural boundary, whose width tends linearly to 0 as tends to the critical value.     

Correlations between clusterization and electrical properties within fluorite-type anions excess solid solutions: Setting of a model

We proposed a model to correlate, in a continuous manner, the composition dependence of electrical properties and the progressive extension of clusterization when the substitution rate increases in a fluoride anion excess CaF₂-type solid solution of M_1–xM _x ²⁺ F_2+x(=1,2,3). A new classification of clusters is given based on the presence or absence of coexistence between two types of interstitial fluoride ions.The second part of the paper is devoted to the representation of the sum of interstitial fluoride ionsn _{F int} and the sum of vacancies in normal sitesn according to the general equationy=(mx ³+qx)/(x ²+q). This model allows us to correlate the structural and electrical properties of a large number of solid solutions with fluorite-type structure.     

Long-range order in the XXZ model

The existence of long-range order is proved under certain conditions for the antiferromagnetic quantum spin system with anisotropic interactions (XXZ model) on the simple cubic or the square lattice. In three dimensions (the simple cubic lattice), finite long-range order exists at sufficiently low temperatures for any anisotropy(0) ifS1, and for 0<0.29 (XY-like) or>1.19 (Ising-like) ifS=1/2. In two dimensions (the square lattice), ground-state long-range order exists under the following conditions: for any anisotropy (0) ifS3/2; 0<0.032 (XY-like) or 0.67<<1.34 (almost isotropic) or>1.80 (Ising-like) ifS=1;>1.93 (Ising-like) ifS=1/2. We conjecture that the two-dimensional spin-1/2XY model (=0) has finite ground-state long-range order. Numerical evidence supporting this conjecture is given.     

Vector two-point functions in maximally symmetric spaces

We obtain massive and massless vector two-point functions in maximally symmetric spaces (and vacua) of any number of dimensions. These include de Sitter space and anti-de Sitter space, and their Euclidean analogsS ⁿ andH ⁿ. Our method is based on a simple way of constructing every possible maximally symmetric bitensorT _a...bc...d(x, x) which carries tangent-space indicesa...b atx andc...d atx.     

Effect of plastic deformation on precipitation in Al-30 wt.% Zn alloy aged at 200 °C

The electron microscopic investigation of an Al-30 wt.% Zn alloy reveals that the plastic deformation of quenched samples substantionally modifies the phase transformation processes examined in the alloy aged at 200°C. Whereas the growth kinetics of metastable precipitates and associated solute diffusion are unaffected by cold rolling the alloy specimens from 9% up to 97·5% reduction in thickness, the rate of all observed transformations is enhanced considerably by prior plastic deformation. A corresponding increase of stored strain energy within the lattice provides namely an additional driving force for the establishment of a new precipitate/matrix interface of higher surface energy on the transformation of a metastable precipitate into a more stable one. The sizes of transforming transition precipitates consequently diminish with an increase of cold work and the respective transformations are thus accelerated.High dislocation density in heavily cold worked alloy also reduces the nucleation barrier for a heterogeneous nucleation on dislocations. The formation of platelike coherent_coh precipitates with internal cubic structure on dislocations is observed followed by the transformation of_coh into spheroidical semicoherent precipitates. The non-uniform distribution of stresses and strains in cold rolled specimens leads to the development of deformation bands in the higher strained regions of even lightly deformed alloy. The direct precipitation of equilibrium precipitates in deformation bands is already observed immediately after cold work analogously to the -allotriomorph formation at grain boundaries.     

Ising Models on Hyperbolic Graphs II

We consider Ising models with ferromagnetic interactions and zero external magnetic field on the hyperbolic graph (v, f), where v is the number of neighbors of each vertex and f is the number of sides of each face. Let T _c be the critical temperature and T _c =supTT _c: ^f=( ⁺+ ^–)/2, where ^f is the free boundary condition (b.c.) Gibbs state, ⁺ is the plus b.c. Gibbs state and ^– is the minus b.c. Gibbs state. We prove that if the hyperbolic graph is self-dual (i.e., v=f) or if v is sufficiently large (how large depends on f, e.g., v35 suffices for any f3 and v17 suffices for any f17) then 0<T _c <T _c, in contrast with that T _c =T _c for Ising models on the hypercubic lattice Z ^d with d2, a result due to Lebowitz.⁽²²⁾ While whenever T<T _c , ^f=( ⁺+ ^–)/2. The last result is an improvement in comparison with the analogous statement in refs. 28 and 33, in which it was only proved that ^f=( ⁺+ ^–)/2 when TT _c and it remains to show in both papers that ^f =( ⁺+ ^–)/2 whenever T<T _c . Therefore T _c and T _c divide [0, ] into three intervals: [0, T _c ), (T _c , T _c), and (T _c, ] in which ^{+ –} but ^f =( ⁺+ ^–)/2, ^{+ –} and ^f ( ⁺+ ^–)/2, and ⁺= ^–, respectively.     

The intersection of Brownian paths as a case study of a renormalization group method for quantum field theory

A new approach is presented for the study of the probability that the random paths generated by two independent Brownian motions in ^d intersect or, more generally, are within a short distancea of each other. The well known behavior of that function ofa-above, below, and at the critical dimensiond=4, as well as further corrections, are derived here by means of a single renormalization group equation. The equation's derivation is expected to shed some light on the -function of the _d ⁴ quantum field theory.Sloan Foundation Research Fellow. Research supported in part by NSF grant PHY-8301493     

Temperature Dependence of the Gibbs State in the Random Energy Model

We consider the problem of temperature dependence of the Gibbs states in two spin-glass models: Derrida's Random Energy Model and its analogue, where the random variables in the Hamiltonian are replaced by independent standard Brownian motions. For both of them we compute in the thermodynamic limit the overlap distribution ^N _{i=1 i i} /N[–1,1] of two spin configurations , under the product of two Gibbs measures, which are taken at temperatures T,T respectively. If TT are fixed, then at low temperature phase the results are different for these models: for the first one this distribution is D _{0 0}+D _{1 1}, with random weights D ₀, D ₁, while for the second one it is ₀. We compute consequently the overlap distribution for the second model whenever T–T0 at different speeds as N.